Cut the chard stems into 1/2-inch pieces and the leaves into 1-inch pieces; keep separate. Toast the caraway and cumin seeds in a skillet over medium heat, 1 to 2 minutes. Cool, then grind in a spice grinder or transfer to a resealable plastic bag and crush with a heavy skillet.
Heat the olive oil in a large pot over medium heat. Add the chard stems and onion and cook until softened, 5 to 6 minutes. Clear a space in the pan, then add the tomato paste, harissa, garlic and ground spices. Cook 2 minutes, then stir into the vegetables. Add the chard leaves, chicken broth and 1 cup water, bring to a rapid simmer and cook until the chard is tender, about 10 minutes. Squeeze in the juice from 1/2 lemon and season with salt.
Mix the yogurt, the juice from the remaining 1/2 lemon and a pinch of salt. Divide the soup among bowls. Add the eggs, pita chips and a dollop of the yogurt mixture; drizzle with olive oil.